Question

the sum of the interior angles in a polygon is 3,240°. how many sides are in the polygon?

Explanation:

Step1: Recall the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides.

Step2: Substitute the given sum into the formula

We know that \(S = 3240^{\circ}\), so \(3240=(n - 2)\times180\).

Step3: Solve for \(n\)

First, divide both sides of the equation by \(180\): \(\frac{3240}{180}=n - 2\).
Since \(\frac{3240}{180}=18\), the equation becomes \(18=n - 2\).
Then, add \(2\) to both sides: \(n=18 + 2\).

Answer:

\(20\)